After discussing some basic facts about generalized module maps, we use the
representation theory of the algebra of adjointable operators on a Hilbert
B-module E to show that the quotient of the group of generalized unitaries on E
and its normal subgroup of unitaries on E is a subgroup of the group of
automorphisms of the range ideal of E in B. We determine the kernel of the
canonical mapping into the Picard group of the range ideal in terms of the
group of its quasi inner automorphisms. As a by-product we identify the group
of bistrict automorphisms of the algebra of adjointable operators on E modulo
inner automorphisms as a subgroup of the (opposite of the) Picard group.Comment: minor corrections, some parts extended, this version is to appear in
Proceedings of the Indian Academy of Science
